Generalized Pell-Padovan Numbers
Yüksel Soykan *
Department of Mathematics, Faculty of Art and Science, Zonguldak Bülent Ecevit University, 67100, Zonguldak, Turkey.
*Author to whom correspondence should be addressed.
Abstract
In this paper, we investigate the generalized Pell-Padovan sequences and we deal with, in detail, four special cases, namely, Pell-Padovan, Pell-Perrin, third order Fibonacci-Pell and third order Lucas-Pell sequences. We present Binet’s formulas, generating functions, Simson formulas and the summation formulas for these sequences. Moreover, we give some identities and matrices related with these sequences.
Keywords: Pell-Padovan numbers, Pell-Perrin numbers, third order Fibonacci-Pell numbers, third order Lucas-Pell numbers.